Dental Mirror. A dentist uses a curved mirror to view teeth on the upper side of the mouth. Suppose she wants an erect with a magnification of 2.00 when the mirror is 1.25 cm from a tooth. (Treat this problem as though the object and lie along a straight line.) (b) What must be the focal length and radius of curvature of this mirror?

Video transcript

Welcome back. Everyone. We are told that a student would like to get a virtual image three times larger than the size of a penny, which means that our magnification constant is going to be positive three. Now the student placed the penny five cents meters away from a concave mirror with a focal length F. We are tasked with finding what is that focal length and what is going to be the radius of curvature of the mirror in order to satisfy the student's requirements. Well, what we can go ahead and say is that our magnification constant is simply equal to the negative of the position of the image divided by the position of the object. What this gives us is that the position of the image is equal to negative three times that the position of the object. The reason we wanted to establish this the quality is because we have a relationship between the position of the object position of the image and the focal length as follows one over the position of the object plus one over the position of the image is equal to one over the focal length rearrange changing for our focal length. What this gives us is that our focal length is equal to S times S prime divided by S plus S prime. But we can go ahead and sub in for S prime negative three S. What this gives us is S times negative three S divided by S minus three S. This simplifies down to having a focal length of 1.5 times the position of the object, which is simply 1.5 times five, giving us a focal length of 7.5 centimeters. Now, what about the radius? Well, we know that the focal length is simply the ra divided by two, which means that our radius is going to be two times our focal length. This gives us two times 7.5 giving us a radius of 15 centimeters. So now we have found both the focal length and the radius corresponding to our final answer. Choice of D Thank you all so much for watching. I hope this video helped. We will see you all in the next one.